He appears in Downton Abbey, one of a wave of TV dramas centred on class, and in the Radio Times this week the actor Rob James-Collier was asked whether working-class talent was being squeezed out of the profession. James-Collier was born in Stockport, and defines himself as working class, and his answer was direct. As with so many other jobs at the moment, he said, you have to work for no money when starting out, and "how on earth are you going to finance that" if you don't come from a wealthy background?

His comments tapped into a question that has arisen repeatedly this year. Can anyone but the exceptionally well-heeled, wealthy, connected upper classes now make it in the arts? In acting, in particular, the question was thrown into sharp relief in January, when the shortlist for the Bafta rising star award was announced. The list was remarkable for two reasons. All five nominees were men, and two were contemporaries at one school. Tom Hiddleston and Eddie Redmayne are both old Etonians, and their nomination led to articles highlighting just how their schoolmates are dominating our stages and screens. There's Harry Lloyd, who starred in Great Expectations and The Iron Lady; Harry Hadden-Paton, currently in She Stoops to Conquer at the National Theatre; Damian Lewis, appearing in the hit TV drama Homeland; and Dominic West, star of The Wire and The Hour. That's not to mention Benedict Cumberbatch, who went to Harrow, and Henry Cavill, star of the latest Superman film, who went to Stowe.

Their success raises these issues. Do you need family wealth in order to become an actor? And is there currently a bias towards a certain class in casting? (Are we, to put it simply, buried deep in an era of floppy-fringed costume drama?)

The cost of acting training has long seemed impossibly high, but the introduction of fees at universities in much of the UK might actually make it seem slightly more affordable – not because the situation has improved for acting students, but because it is just so bleak for almost everybody. Vicky Taylor, marketing and communications manager at the Royal Academy of Dramatic Art (Rada) in London, says it costs £9,000 a year for its three-year BA, and £10,000 a year for its MA, but stresses that admission is purely on the basis of talent. There are 3,000 applicants for 28 places each year on the BA, and she says the best get in, regardless of wealth – a system of bursaries and scholarships cover training if an applicant can't afford it.

"What we strive for," she says, "is to train talent and that is the overarching factor for anyone who applies and gets in. You don't have to have had experience. You don't have to have gone to a stage school on a Saturday [during your teens] that you've had to pay for. We audition every single person who applies." Around 57% of Rada's students receive some form of scholarship or bursary fund, she says, and more than a third come from households with a parental income of less than £25,000.

Anna Faulkner, communications and events manager at the Central School of Speech & Drama, also in London, says one of the factors that influences applicants is "whether their secondary school embraces the teaching of performing arts". Central holds performing arts workshops in secondary schools in "lower-participation" areas, she says, which sounds like a great scheme, and apparently broadens interest around the UK.

But even the best schemes are unlikely to be able to compete with the environment at Eton, where the drama department includes a full-time designer, a carpenter, a manager, a part-time wardrobe mistress and a director-in-residence. In the first two months of this year, the school has staged productions of The Cripple of Inishmaan, Attempts on Her Life, The Front Page and The History Boys.

Even if the costs of acting training are covered, the outlook for actors after university is generally tough unless they have a lot of luck, or splendid connections. A few decades back, says Martin Brown, assistant general secretary of the actors' union Equity, there was the possibility of joining a repertory company "that would work at one theatre over a period of six months, sometimes even longer, doing a whole range of productions. Someone coming out of a college such as Rada in those days could reasonably hope to get a job working in a small part, hone their skills, get some income, and that gave them their first footing in the industry. That virtually doesn't exist any more, so people are much more vulnerable. So yes, of course, private income, private wealth, would help enormously to survive."

Andrew Glen, an actor in his late 20s, came out of the Royal Scottish Academy of Music and Drama in Glasgow with debts, and has worked a variety of jobs to get by since – but he sees this experience as highly positive. "I've actually said in letters to casting directors recently that I've done everything from being a bus conductor to working in a factory, being a waiter, and you can draw on all those things. Your next part could be as a person working in a chicken factory, so I think it's enhanced my acting, in a way."

This echoes James-Collier's comment that "because you've done the horrible jobs it gives you an even grittier determination to succeed. If I had a comfort blanket, I wouldn't have been as passionate and driven. It takes away that determination and then, when you get there, you really do appreciate it because you know where you have been."

"I don't think it would make you a better actor if you came from a wealthy background and sat on your arse all day waiting for your agent to get you a job," says Glen. "I think it's better to be interacting with people. Because in the acting profession, that's what it's all about. It's about reacting to whatever circumstance you're in."

It is also about stamina and self belief, and it is in this last quality particularly that a wealthy background perhaps helps. "You need drive, you need courage, you need bravery," says Brown. "You've got to have that self-belief to keep going. Actors, even well-known actors, go to auditions, castings, meetings, and are constantly told: 'No thanks, not you.' Getting turned down is absolutely part of the warp and weft of their lives, so you've got to have that bravery and belief in yourself, and that commitment to keep going." All kinds of people have these qualities, of course, but they are exactly the sort of characteristics that a public-school education is expected to imbue.

I ask Gareth McLean, a TV critic at the Radio Times, who interviewed James-Collier, whether we are in an era of distinctly upper-class drama, a wave of period pieces that an Old Etonian might be particularly well suited to. (All actors want to avoid typecasting, but it goes on. Last year Cumberbatch said as "a posh actor in England, you can't escape class-typing, from whatever side you look at it. I realised quite early on that, although I wasn't trying to make a career speciality of it, I was playing slightly asexual, sociopathic intellectuals".)

McLean says the real problem is how rare it is to see working-class lives on TV. In the past, he says, "there were programmes such as Clocking Off, Auf Wiedersehen Pet and Boys from the Black Stuff, and where are those shows now? The only time you see working-class life on TV is when they go back to people's houses on The X Factor or Britain's Got Talent."

Brown emphasises that "actors still come from a whole range of social backgrounds, and some of them with enormous talent" And it is true that the Bafta rising star award eventually went to Adam Deacon, who said the prize was "a win for the underdog".

It is also true that a wealthy background probably makes it easier to thrive in this risky business. When it comes to that, nothing changes.

Theo Bosanquet: Old Etonians such as Tom Hiddleston and Eddie Redmayne are just the half of it. The costs of entering the profession mean that theatre is in danger of becoming a playground for the privileged